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arXiv · 2008.04304

A Generalization of the Kramers-Kronig Relations for Linear Time-Varying Media

Diego M. Solís·Nader Engheta
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Abstract

We explore the mathematical theory to rigorously describe the response of media with linear time-varying, generally dispersive, electromagnetic constitutive parameters. We show that even when the temporal inhomogeneity takes place on a time scale comparable or shorter than the driving fields' time period, one can still define a physically meaningful time-varying dispersion. Accordingly, a generalized set of Kramers-Kronig relations is investigated to link the real and imaginary parts of the time-varying frequency-dispersive spectra characterizing the medium's constitutive response. Among others, we study the case of a Lorentzian dielectric response with time-varying volumetric density of polarizable atoms and present the varying circuital equivalents of the governing differential equation, which in turn allow us to use the notion of generalized time-varying impedances/admittances of a time-dependent resistor, inductor and capacitor.

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Diego M. Solís, Nader Engheta. 2020-08-10. A Generalization of the Kramers-Kronig Relations for Linear Time-Varying Media. https://doi.org/10.1103/physrevb.103.144303

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